Spreading of quasimodes in the Bunimovich stadium
We consider Dirichlet eigenfunctions uλ of the Bunimovich stadium S, satisfying (∆ − λ²)uλ = 0. Write S = R ∪ W where R is the central rectangle and W denotes the “wings,” i.e., the two semicircular regions. It is a topic of current interest in quantum theory to know whether eigenfunctions can concentrate in R as λ → ∞. We obtain a lower bound Cλ⁻² on the L² mass of uλ in W, assuming that uλ itself is L²-normalized; in other words, the L² norm of uλ is controlled by λ2 times the L² norm...[Show more]
|Collections||ANU Research Publications|
|Source:||Proceedings of the American Mathematical Society|
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